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Longitude by Lunars

"Lunar Distances" or lunars for short were used to determine longitude at sea in the period from about 1767 until 1850 (and rarely after that date). This was a time when chronometers were not yet widely available at a reasonable price and were considered unreliable on long voyages. The principle behind lunars is simple. The Moon in the sky is the hour hand of a great clock. The stars along its path are the numbers on the face of the clock. If we can measure the Moon's position relative to the stars, we can read the time from the clock. Comparing that absolute time with local time, usually determined by a time sight, we have our longitude. A one hour difference in time corresponds to a 15 degree difference in longitude.


15 posted.

Tony Fletcher wrote: 12/8/2013
During Drakes voyage around the world 1577 to 1580 did he ever calculate his longitude ?
He observed a partial eclipse of the moon but did not record his
longitude . I calculate it to be 75west.
Some historians say he calculated it by lunars while at Point Reyes
again it is not recorded
your thoughts please
Frank Reed wrote: 12/8/2013
Hello Tony.

There were occasional attempts to determine longitude by early forms of lunar observations on many voyages before the development, in the late 18th century, of the proper methodology of "lunars". Unfortunately, in nearly every case that I have seen, the methods used in those earlier examples are highly flawed and nearly useless for longitude. I've never looked specifically at Drake's voyage, but I would be happy to discuss it further if you have any details.

To determine longitude by a "lunar-like" observation, two things are needed:
1) a specifically recorded event involving the Moon's position in the sky, for example, the measurement of an actual "lunar distance" (the exact angle between the Moon and Sun or a star), or an observation of an occultation of a star, or an observation of a specific and well-defined event in a lunar eclipse.
2) an observation for local time that is nearly coincident with the first observation (of the Moon's position). This can be any observation of the altitude of the Sun or a star so long as it is well away from the meridian. This observation determines, what we might call, "sundial time". Without this second observation, which was often poorly understood historically, the first observation is nearly useless. Longitude is proportional to the difference between this local "sundial time" and the absolute time provided by the observation of the Moon's position.

It's worth noting that lunar observations for mapping, as opposed to "live" navigation, did not require a Nautical Almanac or proper "lunar theory". If the observations above were taken and recorded competently, they could be converted into an accurate longitude after the voyage by comparing against similar observations made at nearly the same time back in England, or any other comparison location. Unfortunately, few experimenters in navigation seem to have understood this point historically. So instead we find navigators attempting to work out longitudes on-site using the very flawed lunar motion models available before the 1760s. This was usually hopeless, resulting in longitudes in error by 10 degrees or more. But when they did record their observations in detail, and so long as those observations met the criteria for the two types of time above, then it's possible to work out relatively accurate longitudes even today.

Your suggestion that Drake's longitude on some date could be found from lunar eclipse observations is certainly reasonable. Whether an accurate longitude can come out of that depends on whether we can reliably determine the specific eclipse event that was observed, and equally important, whether there was some attempt to determine accurate local time simultaneously. As for a lunar longitude near Point Reyes, this probably falls in the category of wishful thinking. A standard "lunar" (in the 18th/19th century sense) was simply impossible in the late 16th century.

Frank Reed
Conanicut Island USA
Tony Fletcher wrote: 12/10/2013
Thank you for your comments
Drakes observation of a partial eclipse of the moon was after he had passed through the Magellan passage into the Southern Ocean It was observed at " 6 o 'clock in the evening and lasted two hours. Golden Hind was in a very bad storm at the time and Drake had much to occupy himself with at the time . Subsequently using the NASA web sight to from the time of the eclipse at London it was at 2300 hence I arrived at Drake's longitude of 75W.
Bawlf in "Secret Voyage of Sir Francis Drake" claims based or unsupported evidence that Drake set up an point of position in the Point Reyes area . This has been hotly denied by other historians .
AS you say it is unlikely that astronomers in the 16th Century had the skills or equipment to carry out lunar observations even on land . Gallileo did not invent the telescope until thirty years after Drake's voyage .
I am a Master Mariner and have PhD in history and am very interested in pre Harrison navigation methodology . Besat Regards and a Happy Christmas Tony Fletcher
piero wrote: 2/10/2014
dear frank , just a trivial question about lunar distance : as the maximum angle for a sextant is 120°, the method for longitude calculation is not applicable when that is greater , isn't ?
Roger Southin wrote: 3/1/2014
A new book just released The Secret Voyage of Sir Francis Drake" by Samuel Bawf. In 1579 Drake had been up the western coast of NA north of Vancouver Island. On his way back down he stopped at Nehalem 30 miles south of the Columbia river and there he set up astronomical observations on the shore using the "Lunar" method to calculate his longitude. He was not very accurate recording 140 degrees versus the actual 124. He was using "Bourne's" method (see pages 10-312
George Goldsteen wrote: 3/26/2014
Dear Mr. Reed,
I noted your comment to Tony Fletcher that using lunar distances to determine longitude prior to about 1760 led to errors in Longitude of 10 degrees or more. I am a retired mariner, hydrographer and lecturer in these fields. The latter in Tasmania, which, as a former Dutchie, made me interested in Abel Tasman's voyage of discovery in 1642/43.

I recently obtained a copy of his logbook. The authors modernised Tasman's Dutch to modern Dutch to facilitate understanding what he wrote. Assuming they did this correctly I am amazed by the accuracy of his longitudes, at least of those near the coast of Tasmania (I have not attempted to check his positions in other locations on his voyage).

He almost daily (depending on whether the skies were clear enough) enters in his log that he measured his latitude and longitude and compass error. On days when he could not observe he calculated his position by Dead Reckoning. He used a variety of expressions w.r.t. how he obtained his position. E.g. "at noon we had the altitude of 41 degrees 15 minutes, longitude 172 degrees 35 minutes, course made good East and sailed 40 miles." Note that his miles equal exactly 4 nautical miles.
In the introduction by the authors no mention is made of Tasman's navigational methods, except to say that he used the Meridian of Tenerife as his Zero Meridian. It lies 16d39m West of the Greenwich Meridian. I automatically assumed he used lunar distances, but of course he could not possibly use these every day for the simple reason of course that the Moon is not always visible during the day, whereas it is obvious from Tasman's log he always obtained noon positions and always had a longitude and no mention is ever made of obtaining a fix at night.

My question to you: Do you have any idea what method Tasman used to determine his position ?
Kind Regards,
George Goldsteen
G Pedro Kinner wrote: 10/5/2014
My family traveled by wagon from Indiana to California in 1848 may 1 thru sept 5 along California trail and 1st wagons over Carson pass I know the campsites now and would like to add the moon phases and sunrise and sunsets. Where can I find this. Thanks
Frank Reed wrote: 10/5/2014
Mr. Kinner,

There are many ways to get that information, and I would be happy to help.
Evangelos Kontos wrote: 11/4/2014
Hello! I would like to ask you what DR Lat and DR Lon means at Predicted Geocentric Lunar Distances? If I wanted lunar distances at Greenwich I would put 0.00 at DR Lon? And what about DR Lat? Thank you in advance!
Frank Reed wrote: 11/4/2014
Hello Evangelos Kontos,

The entries on the lunar distance prediction page for DR lat and lon only matter if you select "Visible at DR Only". This is just for planning purposes. For example, if you wanted to practice shooting lunars tonight, you would not be interested in cases that cannot be seen from your position. Otherwise, the lat and lon data have no effect since the calculated distances are "geocentric". You can experiment with a couple of cases and verify this. Thanks for your question!

Frank Reed
Evangelos Kontos wrote: 11/5/2014
Ok! So, if I select GMT the lunars calculated refer to Greenwich meridian, right?
Frank Reed wrote: 11/5/2014
Hello Evangelos,


Frank Reed
Evangelos Kontos wrote: 11/8/2014
Hello Mr Reed. I want to apply a different method to get the lunar and I want your help...again! do you know where I can find the correction tables for refraction? I only have an internet version of Nautical Almanac in which they are not included. In this same N.A there is a formulae for dip: 1.758*HT^1/2, HT in meters. 1.758 is minutes of a degree? Finally, we get the observed (apparent) altitude of moon and stars after the correction for dip and SD or before? In other words, the corrected altitudes are about refraction and parallax only? Or dip and SD must be considered? Thank you in advance, I am obliged.
Evangelos Kontos wrote: 11/20/2014
Dear Mr Reed, how can I find HP of moon at any local time? The nautical almanac lists HP for GMT. Thanks in advance.
Frank Reed wrote: 11/21/2014

I would recommend that you read my little essay, linked above, entitled "Easy Lunars". That should address most of your questions. If not, please get back to me. For Nautical Almanac tables, there is a copy of one from 1994 in the downloads section here: Naturally, the positions of the celestial bodies were only correct for that year, but the refraction tables and other "permanent" data are still valid.

As for the HP being listed for GMT, this is no different from any other quantity in the almanac!! All you have to do is convert your local mean time to GMT by adding or subtracting the appropriate number of hours. Honestly, that's trivial.

Incidentally, if you have not already looked, you might really benefit from asking your questions on the NavList message boards at Anyone who is anyone in the world of celestial navigation (such as it is in the 21st century) posts there.

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